See the pre-processing in the article (page 9) :

https://www.researchgate.net/publication/3321188_Two_decades_of_array_signal_processing_research_the_parametric_approach

Article Two Decades of Array Signal Processing Research: The Paramet...

what do mean by coherent DOA estimation. can u elaborate a bit more?

Spatial Smoothing. Please refer to the attachment.

By recording signal strength and data transfer rate together and calculating correlation coeff.

What do you mean, Satyendra ?

MATLAB codes: the MUSIC algorithm and the improved MUSIC algorithm for coherent signals

1-The MUSIC algorithm for coherent signals

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

clc

clear all

format long

N=200;

doa=[20 60]/180*pi;

w=[pi/4 pi/4]';

M=10;

P=length(w);

lambda=150;

d=lambda/2;

snr=20;

D=zeros(P,M);

for k=1:P

D(k,:)=exp(-j*2*pi*d*sin(doa(k))/lambda*[0:M-1]);

end

D=D';

xx=2*exp(j*(w*[1:N]));

x=D*xx;

x=x+awgn(x,snr);

R=x*x';

[N,V]=eig(R);

NN=N(:,1:M-P);

theta=-90:0.5:90;

for ii=1:length(theta)

SS=zeros(1,length(M));

for jj=0:M-1

SS(1+jj)=exp(-j*2*jj*pi*d*sin(theta(ii)/180*pi)/lambda);

end

PP=SS*NN*NN'*SS';

Pmusic(ii)=abs(1/ PP);

end

Pmusic=10*log10(Pmusic/max(Pmusic));

plot(theta,Pmusic,'-k')

xlabel('angle \theta/degree')

ylabel('spectrum function P(\theta) /dB')

title('DOA estimation based on MUSIC algorithm')

grid on 47

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

2-The improved MUSIC algorithm for coherent signals

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

clc

clear all

format long

N=200;

doa=[20 60]/180*pi;

w=[pi/4 pi/4]';

M=10;

P=length(w);

lambda=150;

d=lambda/2;

snr=20;

D=zeros(P,M);

for k=1:P

D(k,:)=exp(-j*2*pi*d*sin(doa(k))/lambda*[0:M-1]);

end

D=D';

xx=2*exp(j*(w*[1:N]));

x=D*xx;

x=x+awgn(x,snr);

R=x*x';

J=fliplr(eye(M));

R=R+J*conj(R)*J;

[N,V]=eig(R);

NN=N(:,1:M-P);

theta=-90:0.5:90;

for ii=1:length(theta)

SS=zeros(1,length(M));

for jj=0:M-1

SS(1+jj)=exp(-j*2*jj*pi*d*sin(theta(ii)/180*pi)/lambda);

end

PP= SS*NN*NN'*SS';

Pmusic(ii)=abs(1/ PP);

end

Pmusic=10*log10(Pmusic/max(Pmusic));

plot(theta,Pmusic,'-k')

xlabel('angle \theta/degree')

ylabel('spectrum function P(\theta) /dB')

title('DOA estimation based on MUSIC algorithm')

grid on

Dear Mushtaq,

As explained by Prof. Harkouss, the improved MUSIC algorithm he shared includes forward-backward smoothing (which is a trick by providing double spatial subarrays to smooth over). The backward smoothing is done as he wrote:

R=R+J*conj(R)*J; where J is the backward identity

This aformentioned step is referred to as backward smoothing. 

Please refer to the attachment for more info

Can spatial smoothing or backward forward averaging be applied to arbitrary array configuration without array manifold interpolation?

Dear Martin,

The answer is in general No ..

For example in a Uniform linear Antenna (ULA) Array setting, the good thing is that the difference between any two overlapping subarrays is a phase difference. Thus smoothing could be applied.

In a circular antenna array, it is NOT. But, there was some work done on circular antenna arrays (1990s) in which they could, indeed, be pre-processed to form a virtual ULA, where afterwards the smoothing remedy could be applied.

Thank you, I have the same info but wasn't sure if I missed something.

Cheers

No problem !! 

Hello Dear,

For coherent signals (from a source due to multipath fading) or correlated sources you should do a pre-processing. It means you have to change correlated signals to uncorrelated. To do this, one solution is spatial smoothing. Forward-Backward spatial smoothing is the best one. For more details you can see following references:

Shahriar Shirvani Moghaddam, Ali Janan, “Performance Evaluation of 2-D DOA Estimation Algorithms in Noisy Channels,” International Journal of Sensors, Wireless Communications and Control (IJSWCC),” Vol. 3, No. 2, pp. 95-100, Dec.2013.

Shahriar Shirvani Moghaddam, Somaye Jalaei, “Determining the Number of Coherent Sources Using FBSS-based Methods,” Frontiers in Science, Vol. 2, No. 6, pp. 203-208, December 2012.

I agree with Shahriar

Depends on what methods you want to use and what arrays you use. For example, if you want to use subspace methods, then you need to exploit some shift-invariance properties in the arrays. Then you need to look at the arrays that you use. If there is naturally a shift-invariance strcture in the array, like ULA and EM vector-sensor array, it can be easily be done via smoothing. If there is none such array, you may switch to the temporal structure or high-order statistics of the sources to look for this shift-invariance  structure. If you use large scaled array, maybe you don't need to do anything on the source dimension, instead, you may want to do hankelization on the space mode and use tensors. I think there are plenty of methods to deal with coherence, and this is totally dependent on the specific applications.

In many applications, we need high resolution estimation of DOAs.

For this purpose, many high resolution subspace-based algorithms

such as MUSIC  and ESPRIT  have been proposed in the past. A new alternative effective method for DOA estimation for coherent sources has proposed ,which is also computationally efficient as a ( Bartlett - MUSIC ) method . While the algorithm has no limitation on the number of coherent sources , it does not need extra elements either.

 Hence it is expected that this algorithm performs better in multi-path situations

when compared to MUSIC and ESPRIT.

 This method takes advantage of Bartlett and Beamspace MUSIC methods and offers a low computational algorithm for locating the coherent sources.

In this method , Bartlett is used as initial DOA estimator for beamspace MUSIC method. Beamformer section forms a small number of beams in the adjacent region

 of the Bartlett spectrum peaks. Then the outputs of beamformer are applied to MUSIC

  algorithm and finally DOAs are determined with high resolution.

But Bartlett could estimate only one DoA, no ? 

No, the conventional (Bartlett) beamformer, can detect multiple arrivals. The resolution is very low though compared to subspace algorithms.

I must have mixed it with something else. 

Yes, Martin it is true, the beamwidth of Bartlett beamformer is much greater compared to subspace methods.

See the pre-processing in the article (page 9) :

https://www.researchgate.net/publication/3321188_Two_decades_of_array_signal_processing_research_the_parametric_approach

Article Two Decades of Array Signal Processing Research: The Paramet...